The implicit equation of a canal surface

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dc.creatorDohm, Marc
dc.creatorZube, Severinas
dc.date2008-06-25
dc.date.accessioned2026-07-07T12:19:41Z
dc.date.available2026-07-07T12:19:41Z
dc.descriptionA canal surface is an envelope of a one parameter family of spheres. In this paper we present an efficient algorithm for computing the implicit equation of a canal surface generated by a rational family of spheres. By using Laguerre and Lie geometries, we relate the equation of the canal surface to the equation of a dual variety of a certain curve in 5-dimensional projective space. We define the μ-basis for arbitrary dimension and give a simple algorithm for its computation. This is then applied to the dual variety, which allows us to deduce the implicit equations of the the dual variety, the canal surface and any offset to the canal surface.
dc.description26 pages, to be published in Journal of Symbolic Computation
dc.identifierhttps://arxiv.org/abs/0806.4127
dc.identifierhttp://arxiv.org/abs/0806.4127
dc.identifierdoi:10.1016/j.jsc.2008.06.001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212839
dc.subjectAlgebraic Geometry
dc.subjectSymbolic Computation
dc.subjectCommutative Algebra
dc.titleThe implicit equation of a canal surface
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